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Aristotle Gap

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AristotleGap

The term "Aristotle gap"' is introduced in this work to refer to the angle between the first and last member of a 5-tetrahedral ring. This gap has angle measure

theta=2pi-5alpha
(1)
=cos^(-1)((241)/(243))
(2)
=0.1283882... radians
(3)
=7.35610... degrees,
(4)

where

alpha=cos^(-1)(1/3)
(5)

is the dihedral angle of the regular tetrahedron.

The fact that theta!=0 is a refutation of an assertion by Aristotle that regular tetrahedra fill space (Aristotle 1939, p. 319; Lagarias and Zong 2012).

See also

Tetrahedral Ring

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References

Aristotle. Book III.8 in On the Heavens (Trans. W. K. C. Guthrie). Cambridge, MA: Harvard University Press, 1939.Doye, J. P. K. "A Model Metal Potential Exhibiting Polytetrahedral Clusters." 21 Jan 2003. https://arxiv.org/abs/cond-mat/0301374.Lagarias, J. C. and Zong, C. "Regular Tetrahedra." Not. Amer. Math. Soc. 59, 1540-1549, 2012.

Cite this as:

Weisstein, Eric W. "Aristotle Gap." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AristotleGap.html

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